Vol. 33
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2013-10-14
Hybrid FEM-Fmm Approach for Efficient Calculations of Periodic Photonic Structures
By
Progress In Electromagnetics Research M, Vol. 33, 121-135, 2013
Abstract
A hybrid approach to find the optical response of periodic photonic structures to incident light is presented. The approach is based on a scattering matrix combination of the Finite Element Method (FEM) and the Fourier Modal Method (FMM). Optical response calculations include: scattering in both reflection and transmission directions, absorption and electric and magnetic field distributions inside the structure. The approach is tested on a structure --- composed of dielectric and metallic materials --- that is periodic in one direction. An analysis of the calculation accuracy shows that the approach depends on the subdivision into FEM and FMM domains and that the optimal subdivision depends on the calculations frequency range as well as on the structure geometry. For testing, we use the commercial FEM solver contained in CST Microwave Studio and a based on C/C++ Fourier Modal Method implementation.
Citation
Alexander Dorodnyy, Valery Shklover, and Christian Hafner, "Hybrid FEM-Fmm Approach for Efficient Calculations of Periodic Photonic Structures," Progress In Electromagnetics Research M, Vol. 33, 121-135, 2013.
doi:10.2528/PIERM13082301
References

1. Hiptmair, R., "Finite elements in computational electromagnetism," Acta Numerica, 237-339, 2002.

2. Li, L. F., "New formulation of the fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A, Vol. 14, 2758-2767, 1997.
doi:10.1364/JOSAA.14.002758

3. Tikhodeev, S. G., A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B, Vol. 66, No. 4, 045102, 2002.
doi:10.1103/PhysRevB.66.045102

4. Christ, A., T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B, Vol. 70, No. 3, 125113, Sep. 2004.
doi:10.1103/PhysRevB.70.125113

5. Hafner, Ch. and R. Ballisti, "The multiple multipole method (MMP)," Compel --- The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 2, No. 1, 1-7, 1983.
doi:10.1108/eb051970

6. Talebi, N., M. Shahabadi, and Ch. Hafner, "Analysis of a lossy microring using the generalized multipole technique," Progress In Electromagnetics Research, Vol. 66, 287-299, 2006.
doi:10.2528/PIER06112801

7. Sannomiya, T. and Ch. Hafner, "Multiple multipole program modelling for nano plasmonic sensors," Journal of Computational and Theoretical Nanoscience, Vol. 7, 1587-1595, 2010.
doi:10.1166/jctn.2010.1523

8. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, 302-307, 1966.

9. Shlager, K. L. and J. B. Schneider, "A selective survey of the finite-difference time-domain literature," IEEE Antennas and Propagation Magazine, Vol. 37, No. 4, 39-57, 1995.
doi:10.1109/74.414731

10. Kagami, S. and I. Fukai, "Application of boundary-element method to electromagnetic field problems," IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 4, 455-461, 1984.
doi:10.1109/TMTT.1984.1132702

11. Buffa, A., M. Costabel, and C. Schwab, "Boundary element methods for Maxwells equations on non-smooth domains," Numer. Math., Vol. 92, 679-710, 2002.
doi:10.1007/s002110100372

12. Komarevskiy, N., V. Shklover, L. Braginsky, and C. Hafner, "Ultrasensitive switching between resonant reflection and absorption in periodic gratings," Progress In Electromagnetics Research, Vol. 139, 799-819, 2013.

13. Deceglie, M. G., V. E. Ferry, A. Paul Alivisatos, and H. A. Atwater, "Design of nanostructured solar cells using coupled optical and electrical modeling," Nano Lett., Vol. 12, 2894-2900, 2012.
doi:10.1021/nl300483y

14. Wilson, E. L. and R. E. Nickell, "Application of the finite element method to heat conduction analysis," Nuclear Engineering and Design, Vol. 4, 276-286, 1966.
doi:10.1016/0029-5493(66)90051-3

15. Petyt, M., J. Lea, and G. H. Koopmann, "A finite element method for determining the acoustic modes of irregular shaped cavities," Journal of Sound and Vibration, Vol. 45, 495-502, 1976.
doi:10.1016/0022-460X(76)90730-6

16. Ko, D. Y. K. and J. C. Inkson, "Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems," Phys. Rev. B, Vol. 38, No. 14, 9945-9951, 1988.
doi:10.1103/PhysRevB.38.9945